The hydrological cycle is expected to intensify under global warming(1), with studies reporting more frequent extreme rain events in many regions of the world(2-4), and predicting increases in future flood frequency(5). Such early, predominantly mid-latitude observations are essential because of shortcomings within climate models in their depiction of convective rainfall(6,7). A globally important group of intense storms-mesoscale convective systems (MCSs) 8-poses a particular challenge, because they organize dynamically on spatial scales that cannot be resolved by conventional climate models. Here, we use 35 years of satellite observations from the West African Sahel to reveal a persistent increase in the frequency of the most intense MCSs. Sahelian storms are some of the most powerful on the planet(9), and rain gauges in this region have recorded a rise in 'extreme'(17) daily rainfall totals. We find that intense MCS frequency is only weakly related to the multidecadal recovery of Sahel annual rainfall, but is highly correlated with global land temperatures. Analysis of trends across Africa reveals that MCS intensification is limited to a narrow band south of the Sahara desert. During this period, wet-season Sahelian temperatures have not risen, ruling out the possibility that rainfall has intensified in response to locally warmer conditions. On the other hand, the meridional temperature gradient spanning the Sahel has increased in recent decades, consistent with anthropogenic forcing driving enhanced Saharan warming(10). We argue that Saharan warming intensifies convection within Sahelian MCSs through increased wind shear and changes to the Saharan air layer. The meridional gradient is projected to strengthen throughout the twenty-first century, suggesting that the Sahel will experience particularly marked increases in extreme rain. The remarkably rapid intensification of Sahelian MCSs since the 1980s sheds new light on the response of organized tropical convection to global warming, and challenges conventional projections made by general circulation models.